Impedance of a cell

The impedances of a cell s leads, contacts and electrolyte solution can be approximated to a situation of impedances in series. Typical values will be Zieads — 1, Zcontacts — 6 and ZQi t).Qiyt0 solution 40 (with all Z values beinq cited at fixed frequency). Calculate the total impedance of these three components when combined together. 

Both impedance and admittance are called immittances. Between other related functions, complex dielectric constant should also be mentioned [78]. It is used in the analysis of dielectric relaxation and is obtained from the measured admittance (impedance) of a cell with a given dielectric (liquid or solid) ... 

The analysis of EN results obtained between two working electrodes (WEs) with an imposed or naturally developing asymmetry can be carried out by considering Eq. (5.27), which indicates that the noise impedance of a cell (Z ) depends on the impedances of the two WEs, as well as their noise levels, represented by the power density spectra (and Pi obtained by performing the analysis of noise signals with either fast Fourier transform (FFT) or with the maximum entropy method (MEM). 

There is another important factor that strongly affects the performance or rate capability of a cell, the internal impedance of the cell. It causes a voltage drop during operation, which also consumes part of the useful energy as waste heat. The voltage drop due to internal impedance is usually referred to as ohmic polarization or IR drop and is proportional to the current drawn from the system The total internal impedance of a cell is the sum of the ionic resistance of the electrolyte (within the separator and the porous electrodes), the electronic resistances of the active mass, the current collectors and electrical tabs of both elec-... 

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

The cathodic reaction is the reduction of iodine to form lithium iodide at the carbon collector sites as lithium ions diffuse to the reaction site. The anode reaction is lithium ion formation and diffusion through the thin lithium iodide electrolyte layer. If the anode is cormgated and coated with PVP prior to adding the cathode fluid, the impedance of the cell is lower and remains at a low level until late in the discharge. The cell eventually fails because of high resistance, even though the drain rate is low. 

FIGURE 12.13 Equivalent circuit for the impedance of a galvanic cell. 

In a number of works, a potentiostatic regime has been used for the experimental and theoretical study of the anodization of aluminum and other valve metals.80 Upon the application of a constant potential step, Va, barrier-forming electrolytes are characterized by a sharp increase in the anodic current to a certain maximum. Both the slope and the maximum are determined by the impedance of the cell circuit. Subsequently, there is a continuous decrease in the anodic current, which is due to oxide growth. The decay of the anodic current can be described by the expression81... 

This circuit is usually referred to as the Randles circuit and its analysis has been a major feature of AC impedance studies in the last fifty years. In principle, we can measure the impedance of our cell as a function of frequency and then obtain the best values of the parameters Rct,<7,C4i and Rso by a least squares algorithm. The advent of fast micro-computers makes this the normal method nowadays but it is often extremely helpful to represent the AC data graphically since the suitability of a simple model, such as the Randles model, can usually be immediately assessed. The most common graphical representation is the impedance plot in which the real part of the measured impedance (i.e. that in phase with the impressed cell voltage) is plotted against the 90° out-of-phase quadrature or imaginary part of the impedance. 

The task of a cell separator is to impede a direct mixing of anolyte and catholyte and to decrease diffusion, but at the same time the migration of ions has to be possible without a too high voltage drop. Naturally, a compromise of these requirements has to be found. 

Equivalent circuit In impedance analyses, a collection of electrical components used to mimic the frequency behaviour of a cell or electrochemical system. 

The mechanism and characteristics of thermal cutoff devices in several prismatic lithium-ion cells was studied by VenugopaF ° by monitoring the impedance at 1 kHz and the open circuit voltage (OCV) of the cells as a function of temperature. All the cells studied contained PE-based separators with a shutdown temperature between 130 and 135 °C. Within this narrow temperature range, the shutdown separators caused a sharp and irreversible rise in impedance of the cell. Single layer PE separators were effective up to around 145 °C, above which they... 

In addition to the possibility of multiple transport paths, our understanding of reaction mechanisms on LSM is further complicated (as with platinum) by pronounced nonstationary behavior in the form of hysteresis of inductive effects. These effects are sometimes manifest as the often-mentioned (but little-documented) phenomenon of burn-in , a term used in development circles to describe the initial improvement (or sometimes decline) of the cathode kinetics after a few hours or days following initial polarization (after which the performance becomes relatively stable). As recently reported by McIntosh et al., this effect can improve the measured impedance of a composite LSMA SZ cathode by a factor of 5 7relative to an unpolarized cathode at OCV." ° Such an effect is important to understand not only because it may lead to insight about the underlying electrode kinetics (and ways to improve them), but also because it challenges the metrics often used to assess and compare relative cell performance. 

Figure 54. Measured (a) and simulated (b) effect of electrode misalignment, (a) Total-cell and balf-cell impedances of a symmetric LSC/rare-earth-doped ceria/LSC cell with nominally identical porous LSC x= 0.4) electrodes, measured at 750 °C in air based on tbe cell geometry shown. (b) Finite-element calculation of tbe total-cell and half-cell impedances of a symmetric cell with identical R—C electrodes, assuming a misalignment of the two working electrodes (d) equal to the thickness of the electrolyte (L). ...

Furthermore, Boukamp and Adler showed that when the electrodes on opposite sides of a cell are different from each other (as they are in a fuel cell), errors may not only involve a numerical scaling factor but also cross-contamination of anode and cathode frequency response in the measured half-cell impedances. For example. Figure 55a shows the calculated half-cell impedance of the cell idealized in Figure 53a, assuming alignment errors of 1 electrolyte thickness. Significant distortion of the halfcell impedances (Za and Zb) from the actual impedance of the electrodes are apparent, including cross-talk of anode and cathode frequency response (1 and 10 Hz, respectively), as well as a... 

Figure 55. Simulated half-cell impedances of the cell shown in Figure 53, calculated using finite-element analysis. (a) Half-cell responses assuming an electrode misalignment dlL equal to 1, as defined in Figure 54c. (b) Half-cell responses assuming perfect electrode alignment [dlL = 0).

From the ratio of the magnitude of the reflection A from the top of the layer to the magnitude of the reference signal A0, and knowing the impedance Z0 of the coupling fluid and the impedance Zs of the substrate, the impedance of the cell is... 

In potentiometry, we measure the emf of a cell consisting of an indicator electrode and a reference electrode. For emf measurements, we generally use a pH/ mV meter of high input impedance. The potential of the reference electrode must be stable and reproducible. If there is a liquid junction between the indicator electrode and the reference electrode, we should take the liquid junction potential into account. 

This circuit is usually referred to as the Randles circuit and its analysis has been a major Feature of AC impedance studies in the last fifty years. In principle, we can measure the impedance of our cell as a Function of Frequency and then obtain the best values of the parameters and by a... 

It is easily argued that, if the voltage measured by the detector D equals zero, the impedance of the cell must be equal to the impedance of the series combination, i.e. Z = Rs and Z" = (coCs) 1. Usually, the values of Rs and Cs needed to balance the bridge vary with the applied frequency as a consequence of the fact that the cell impedance has a frequency dependence different from that of a simple RC series combination. 

A few comments are in order on the probable validity of conclusions based on this equivalent circuit to real cells. Quite simply stated, real cells that are properly designed will have the same properties as dummy cells of the same values of Rs, Ru, and Cdl. Important design features of a cell are (1) equal resistance between all points on the surface of the working electrode and the auxiliary electrode (2) low-impedance reference electrode and (3) low stray capacitance between electrodes, between leads, and to shields. Spherical symmetry is a good, but somewhat inconvenient, method of meeting the first requirement a parallel arrangement also works with planar electrodes. At the very... 

The impedance is dependent on temperature, as can be seen in Figure 4, which shows the area specific resistance (ASR) of a cell as a function of cell temperature for different gas flow rates. For the same cell temperatures, lower ASR was observed for increasing gas flow rates due to the increased gas diffusion near the electrodes that effectively reduced the overpotential resistances [4], Because the anode and cathode are often conductive, the impedance of the cell is dependent largely on the thickness of the electrolyte. Using an anode supported cell structure, a YSZ electrolyte can be used as thin as 10-20 pm or even 1-2 pm [32, 33] as compared to 0.5 mm for a typical electrolyte supported cell [26],... 

The case of a cell in or near a pore presents an excellent geometry for the measurement of impedance since any electrical currents must flow through the pore provided the silicon is suitably insulated. Any movement of the cell will result in a change of the impedance measured between one side of the mem-... 

To understand how some of these electrical interactions work, we must look into the extracellular space between cells. We might imagine these spaces as narrow, fluid gutters (Adey, 1989), no more than 150 A wide, in which float hormones, antibodies, and neurotransmitters and as spaces that are electrically important because of their low impedance compared with the high impedance of the cell membrane. 

That is, in the specific case of electrochemical impedance spectroscopy (EIS), the steady, periodic linear response of a cell to a sinusoidal current or voltage perturbation is measured and analyzed in terms of gain and phase shift as a function of frequency, to, where the results are expressed in terms of the impedance, Z. In this regard, the impedance response of an electrode or a battery is given by... 

Fig. 11.1. A.c. bridge for the measurement of the impedance of electrochemical cells. The bridge is balanced when the current is zero in this case ZCCJR = ZJR2 where Zs = Rs- i/a)Cs. ...

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